Answer:
[tex] C.676.01 \: {in}^{3} [/tex]
step-by-step explanation :
The volume of the composite solid = volume of the cuboid + volume of the rectangular pyramid
Volume of the cuboid
[tex] = L \times B \times H[/tex]
where
[tex]L = 9 \: inches \\ B = 9 \: inches \\ H = 5 \: inches[/tex]
By substitution,
[tex] \implies \: V = 5 \times 9 \times 9[/tex]
[tex]\implies \: V = 405 \: {in}^{3} [/tex]
Volume of rectangular pyramid
[tex] = \frac{1}{3} \times base \: area \times height[/tex]
[tex]\implies \: V = \frac{1}{3} \times \:( L \times B ) \times \: H[/tex]
[tex] L = 9 \: inches \\ B = 9 \: inches \\ s= 11 \: inches[/tex]
We use the Pythagoras Theorem, to obtain,
h²+4.5²=11²
h²=11²-4.5²
h=√100.75
h=10.03
By substitution,
[tex]\implies \: V = \frac{1}{3} \times \:( 9 \times 9 ) \times \:10.0374[/tex]
we simplify to obtain
[tex]\implies \: V =271.0098 \: {in}^{3} [/tex]
Hence the volume of the the composite solid
[tex]=676.01\: {in}^{3} [/tex]
